Eddies in Numerical Models of the Antarctic Circumpolar Current and Their Influence on the Mean Flow

S. E. Best Department of Oceanography, Southampton Oceanography Centre, University of Southampton, Southampton, United Kingdom

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V. O. Ivchenko Department of Oceanography, Southampton Oceanography Centre, University of Southampton, Southampton, United Kingdom

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K. J. Richards Department of Oceanography, Southampton Oceanography Centre, University of Southampton, Southampton, United Kingdom

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R. D. Smith Los Alamos National Laboratory, Los Alamos, New Mexico

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R. C. Malone Los Alamos National Laboratory, Los Alamos, New Mexico

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Abstract

The dynamics of the Southern Ocean have been studied using two high-resolution models, namely the Fine Resolution Antarctic Model (FRAM) and the Parallel Ocean Program (POP) model. Analysis of these models includes zonal averaging at Drake Passage latitudes, averaging along streamlines (or contours of constant sea surface height), and examining particular subregions of the flow in some detail. The subregions considered in the local analysis capture different flow regimes in the vicinity of the Crozet Plateau, the Macquarie–Ridge Complex, and Drake Passage.

Many aspects of the model results are similar, for example, the magnitude of eddy kinetic energy (EKE) in the “eddy rich” regions associated with the large-scale topography. An important difference between the two models is that away from the strong topographic features the level of EKE in POP is 2–4 times greater than in FRAM, giving values close to those observed in altimeter studies.

In both FRAM and POP instability analysis performed over ACC jets showed that baroclinic instability is likely to be the main mechanism responsible for generating EKE. In the case of FRAM this view is confirmed by regional energy budgets made within the ACC. In contrast to quasigeostrophic numerical experiments upgradient transfer of momentum was not found in the whole ACC, or over large subregions of the Southern Ocean. The only place it occurred was in localized tight jets (e.g., the flow northeast of Drake Passage) where the transients are found to transfer kinetic energy into energy of the mean flow. The transient eddies result in a net deceleration of the ACC for the streamwise averaging.

Corresponding author address: Dr. Vladimir O. Ivchenko, Department of Oceanography, The University of Southampton, Southampton Oceanography Centre, European Way, Southampton SO14 3ZH, United Kingdom.

Abstract

The dynamics of the Southern Ocean have been studied using two high-resolution models, namely the Fine Resolution Antarctic Model (FRAM) and the Parallel Ocean Program (POP) model. Analysis of these models includes zonal averaging at Drake Passage latitudes, averaging along streamlines (or contours of constant sea surface height), and examining particular subregions of the flow in some detail. The subregions considered in the local analysis capture different flow regimes in the vicinity of the Crozet Plateau, the Macquarie–Ridge Complex, and Drake Passage.

Many aspects of the model results are similar, for example, the magnitude of eddy kinetic energy (EKE) in the “eddy rich” regions associated with the large-scale topography. An important difference between the two models is that away from the strong topographic features the level of EKE in POP is 2–4 times greater than in FRAM, giving values close to those observed in altimeter studies.

In both FRAM and POP instability analysis performed over ACC jets showed that baroclinic instability is likely to be the main mechanism responsible for generating EKE. In the case of FRAM this view is confirmed by regional energy budgets made within the ACC. In contrast to quasigeostrophic numerical experiments upgradient transfer of momentum was not found in the whole ACC, or over large subregions of the Southern Ocean. The only place it occurred was in localized tight jets (e.g., the flow northeast of Drake Passage) where the transients are found to transfer kinetic energy into energy of the mean flow. The transient eddies result in a net deceleration of the ACC for the streamwise averaging.

Corresponding author address: Dr. Vladimir O. Ivchenko, Department of Oceanography, The University of Southampton, Southampton Oceanography Centre, European Way, Southampton SO14 3ZH, United Kingdom.

1. Introduction

The Southern Ocean plays a very important part in the general circulation of the World Ocean and consequently the global climate system. The Antarctic Circumpolar Current (ACC) is one of the most significant transporters of water mass in the World Ocean and is responsible for the main exchanges of heat, salt, momentum, and energy between the Atlantic, Indian, and Pacific Oceans. The dynamics of the ACC are highly complex and have been found to be strongly dependent upon the interaction between mesoscale eddies, topography, and the mean flow (e.g., McWilliams et al. 1978;Sarukhanian and Smirnoff 1986; Nowlin and Klinck 1986; Gouretski et al. 1987; Treguier and McWilliams 1990; Wolff et al. 1991; Ivchenko et al. 1996, 1997).

Despite advances in the understanding of Southern Ocean dynamics made by these and other studies, many questions remain unanswered. One reason for this is that the Southern Ocean is a particularly remote region with bad weather conditions and sea ice, which makes the collection of in situ data difficult. In such circumstances numerical model studies become useful tools for furthering our understanding of dynamical processes.

The numerical models which have been used to investigate the Southern Ocean can be separated into three main groups, that is,

  • coarse-resolution models

  • quasigeostrophic (QG) eddy-resolving models

  • primitive equation eddy-resolving (or “nearly eddy resolving”) models.

Coarse-resolution models provide important information about the Southern Ocean and ACC dynamics for global scales and are still important for climatic experiments because they allow integrations over very long timescales (hundreds and thousands of years). However, they cannot resolve the transient eddies that have horizontal scales comparable to the Rossby radius of deformation.

Quasigeostrophic eddy-resolving models have allowed zonal channel dynamics, in which the eddies play an important role, to be understood more fully. However, in the Southern Ocean outcropping of density layers occurs in many places and the basic stratification changes dramatically from the Antarctic coast to the subtropical regions. Consequently many features of Southern Ocean dynamics cannot be described by QG equations.

It is therefore necessary to study the dynamics of the Southern Ocean (and the ACC) by using primitive equation models with high resolution. The models of Semtner and Chervin (1988, 1992), the Fine Resolution Antarctic Model (FRAM: see The FRAM Group 1991) and the Parallel Ocean Program (POP) model (Dukowicz and Smith 1994) are of this type. Unfortunately even these models only marginally resolve eddies because their horizontal resolution is still not high enough. Having said this, these models have been found to describe the role of eddies in certain aspects of the dynamics quite successfully. Some important results from these models, as well as other models that have highlighted the importance of eddies in ACC dynamics, are summarized below.

Analysis of FRAM shows that 58% of the total kinetic energy is associated with the kinetic energy of mean flow (KEM) (Ivchenko et al. 1997). The main balance of KEM for the whole domain is between the energy input by the wind stress and its removal by conversion to potential energy. This result supports the view that the ACC is a wind-driven current and also suggests that the wind stress could strongly influence the global thermohaline circulation (Toggweiler and Samuels 1995). Note, this is in contrast to the energy analysis of the Community Modelling Effort (CME) North Atlantic model (Treguier 1992) where the buoyancy term made up less than 20% of the total sink terms.

In FRAM the highest values of kinetic energy (KE) occur in the ACC and in the western boundary areas. Energetic regions are around the Agulhas Current, near the Crozet and Kerguelen Plateaus and to the southeast of Australia (Macquarie–Ridge Complex). Stevens and Killworth (1992) and Ivchenko et al. (1997) have shown that the level of KE in FRAM is everywhere too low compared with observations. The reason for the low level of total KE is because of the level of eddy kinetic energy (EKE), since the value for KEM agrees reasonably well with observations. Stevens and Killworth (1992) estimate that EKE in FRAM is, at best, only about 25% of observational estimates. The distribution of EKE in the POP experiment is similar to that of FRAM in that the highest values occur in the western boundary regions and near the topographic obstacles over and around which the ACC flows (see Figs. 1a,b). An important difference between the two models is that away from strong topographic features the level of EKE is much higher in POP than in FRAM. POP has levels of EKE much closer to TOPEX altimeter estimates (see Fig. 1c). This is particularly true south of the ACC where POP’s EKE is substantially higher than in FRAM. This is almost certainly because FRAM is failing to resolve most of the eddies at these latitudes.

Numerical models, as well as observations, show that the highest local values of EKE occur at places with the highest velocities, and therefore the largest spatial shears. This supports the view that the eddy variability in the Southern Ocean is mainly associated with baroclinic and barotropic instabilities.

Stevens and Ivchenko (1997) have shown that the balance between topographic form stress and wind stress, first suggested by Munk and Palmén (1951), exists with high accuracy in FRAM for a zonally averaged ACC. We shall call the region of the flow bounded by the southernmost and northernmost latitudes of Drake Passage the ACC belt (ACCB) and the region following the path of the ACC the ACC path (ACCP). The vertical penetration of momentum is achieved through the action of interfacial form stress in which the transient eddies provide the greatest contribution (Johnson and Bryden 1989; Marshall et al. 1993; Ivchenko et al. 1996). The southward eddy flux of density is strongly associated with the vertical transfer of stress.

A number of quasigeostrophic models have shown that eddies play an important role in the horizontal redistribution of momentum (McWilliams et al. 1978; Treguier and McWilliams 1990; Wolff et al. 1991). In these studies the lateral Reynolds stress exerted by eddies on the mean flow is found to transfer zonal momentum into the center of the jet (at least in the flat bottom channel case). In other words, energy is transferred from EKE to KEM. Such a process has been called the “negative viscosity” effect. A full kinetic energy analysis of FRAM has shown that this negative viscosity does not occur in an integral sense over the whole ACC domain, but only in some very tight, localized jets (e.g., just east of Drake Passage) (Ivchenko et al. 1997).

From the above discussion it can be seen clearly that mesoscale eddies play an important role in the dynamics of the Southern Ocean.

In this study two near-eddy-resolving models, namely FRAM and POP, are used to try to understand Southern Ocean eddy processes more fully. The main aims of this paper are

  • to determine the mechanisms responsible for the generation of eddies within the ACC. An instability analysis has been carried out for selected quasi-zonal jets in both models. This has been performed to see whether the flow is baroclinically unstable and, if it is, to predict the growth rates, and corresponding wavelengths, of the most unstable waves.

  • to determine the energy cycle for subregions within the ACC in FRAM. The eddy generation and conversion terms are of particular interest. By comparing and contrasting these terms for several subregions the generation mechanisms, energetics, and dynamics of eddies may be understood more completely.

  • to compare and contrast the Southern Ocean EKE distributions of two primitive equation models (FRAM and POP) that have different horizontal/vertical resolutions and surface forcing. In order to see how realistic these eddy fields are, we have also compared both model results with estimates of EKE made from the TOPEX altimeter (see Le Traon et al. 1994).

  • to determine the distributions of momentum and energy of the ACC for both POP and FRAM. These distributions have been calculated in two ways. First, by zonally averaging the unbounded flow at Drake Passage latitudes (ACCB). Second, by streamline averaging along the path of the ACC (ACCP). The latter averaging has been carried out because topography causes the ACC to move away from the zonal ACCB channel for much of its circumpolar path. Indeed, in FRAM the kinetic energy of the ACCB is found to be only a quarter of that in the ACC proper (Ivchenko et al. 1997). One of the most important aims of this analysis is to see whether Reynolds stresses (more precisely the divergence of Reynolds stress) act to accelerate or decelerate the mean zonal flow, and whether the difference in resolution between POP and FRAM makes any difference to this result.

The structure of this paper is as follows. First, the numerical models used in this study are briefly described in section 2. Regional analysis of instability processes in both models and FRAM’s energy budgets are examined in section 3. Analysis of zonal and streamline-averaged properties for both models are presented in section 4. Finally, the significance of the results are discussed, and the main conclusions presented in section 5.

2. The numerical models

a. The Fine Resolution Antarctic Model (FRAM)

FRAM is a British numerical model of the Southern Ocean. It has a horizontal grid spacing of 0.25° lat × 0.5° long and 32 depth levels. This corresponds to an average horizontal grid size of about 27 km and between 20 and 230 m in the vertical. FRAM uses the traditional formulation in the barotropic-mode equation, which requires smoothing of the bottom topography to increase the numerical stability of the model (The FRAM Group 1991).

FRAM is based on the Geophysical Fluid Dynamics Laboratory model developed by Bryan and Cox, which conserves momentum, energy, and tracers. The model domain covers an area from 24°S to the Antarctic coast.

At the northern boundary an open boundary condition has been used (Stevens 1990). FRAM was initialized as a motionless fluid with constant temperature (−2°C) and salinity (36.69 psu) and then relaxed toward the annual-mean Levitus (1982) climatology. This assimilation was stopped after 6 years of the model run, except at the surface where FRAM was relaxed back to the annual average of the Levitus temperature and salinity with a timescale of 1 year. The seasonal climatological winds of Hellerman and Rosenstein (1983) were used and the model was run for 16 years with the last 6 years of integration used for analysis. During this period the energy was in an almost statistically steady state, although the deep temperature and salinity were not in equilibrium (Killworth and Nanneh 1994).

b. The Parallel Ocean Program Model

The Parallel Ocean Program model is a primitive equation high-resolution numerical model developed at the Los Alamos National Laboratory (Dukowicz and Smith 1994; Maltrud et al. 1997, manuscript submitted to J. Geophys. Res.). It covers the whole World Ocean from 78°S to 78°N using a Mercator grid. The horizontal resolution varies from 6.5 km at 78° (North and South) to 31.25 km at the equator and is 15.6 km at 60°. In total the model has 1280 longitude and 896 latitude points for each horizontal slab and has 20 depth levels, which vary from 25 m for the top layer to 550 m in the deep ocean. POP, like FRAM, is a Bryan–Cox model although it uses an implicit free-surface formulation of the barotropic mode, which allows large-scale barotropic inertial–gravity waves to develop. Unlike standard Bryan–Cox models, which use a rigid-lid boundary condition, no smoothing of the bottom topography is required for computational stability (Smith et al. 1992;Dukowicz et al. 1993).

The surface heat fluxes used by the model are based on the recent work of Barnier et al. (1995). Because of ice-cover the heat flux is not available at high latitudes and so the surface is restored to −2°C with a one-month timescale if ice is present. The model’s surface salinity is restored to the monthly Levitus climatology, linearly interpolated to 3-day intervals. Poleward of 70°N or S the model temperature and salinity are relaxed to the annual-mean Levitus climatology from the surface to a depth of 2 km with a 3-month relaxation timescale.

POP uses a biharmonic form of both diffusion and viscosity for the horizontal mixing of momentum and tracers. The coefficients of viscosity and diffusivity both vary spatially as (cosΘ)3, where Θ is the latitude. At the equator the biharmonic viscosity is −0.6 × 1020 cm4 s−1 and the diffusivity is −0.2 × 1020 cm4 s−1. For vertical mixing viscosity and diffusivity are based on the standard Pacanowski and Philander (1981) schemes, which include Richardson number dependence. Background vertical diffusivity is 0.1 cm2 s−1 and viscosity is 1.0 cm2 s−1. For bottom friction, a standard quadratic form, with a coefficient of 1.223 × 10−3, has been used.

Unless otherwise noted, the results presented here are time averages over the last 5 years of a 10-yr simulation, which was the last in a sequence of three simulations passing through the 1985–94 ECMWF winds, each initialized from the final state of the previous run. The first run, called “POP5,” used monthly mean winds and restored to the seasonal climatological temperature and salinity fields of Levitus (1982) in the surface layer (with a 1-month relaxation timescale). The forcing in the second run, “POP7,” was the same as the first except that high-frequency (3-day average) winds were used. The third run (“POP11” used in this study) was the same as the second but used the Barnier et al. (1995) seasonal heat fluxes instead of restoring surface temperature to the Levitus climatology. A detailed description of these three runs is given in Maltrud et al. (1997, manuscript submitted to J. Geophys. Res.).

3. Regional analysis

In order to understand the eddy dynamics of the ACC we have singled out three regions. Results from FRAM and POP in these regions are then contrasted with each other and are also compared with altimeter data. These results, as well as descriptions of the subregions examined, are presented in section 3a. Section 3b presents the results of a regional energy budget calculated for FRAM for the subregions described in section 3a. This analysis has been carried out to identify the main sources of EKE in the various subregions. Section 3c presents the results of an instability analysis performed on a selection of time-mean jets within the ACC in both FRAM and POP. This analysis has been carried out to try to examine the role baroclinic instability plays in selected jets within each model.

a. Description of subregions

The three ACC subregions chosen for detailed study are the flow around Crozet Plateau (Region A), the Macquarie–Ridge complex (Region B), and flow through Drake Passage (Region C) (see Fig. 2).

1) Region A: Crozet Plateau

Crozet Plateau is located at 44°–47°S, 40°–48°E. In this region FRAM produces a flow that separates upstream of the plateau (Fig. 3). Approximately 60 Sv (Sv ≡ 106 m3 s−1) is associated with the northern branch of the flow with around 40 Sv associated with the southern branch. In POP a far greater proportion of the ACC flows to the north and over the plateau with very little flowing south of the plateau. This solution is similar to observational estimates by Park et al. (1993), which suggest that more than 90% of the flow occurs to the north of Crozet Plateau. In both models, a particularly vigorous EKE field is produced in the Crozet Plateau region. In FRAM, this begins just as the flow is constrained to flow southward by the topography between 44° and 46°E. The EKE values are of a similar magnitude in the POP model. There are two main differences between the models, however. First, the level of EKE throughout the region is much greater in POP than FRAM (see Figs. 4a,b). Although maximum values in FRAM are just as high as in POP, these values are restricted around the northern branch and downstream of the plateau. Second, in POP the most vigorous part of the flow occurs almost entirely downstream of the plateau, whereas in FRAM there is also strongly unstable flow around its northern flank.

The eddy field from the TOPEX altimeter data also shows a vigorous eddy field around the northern branch and downstream of the plateau (see Fig. 4c). In regions of high eddy activity the levels of EKE given by the altimeter (expressed as the variance of the geostrophic velocity) and the two models compare well, although the general level of EKE from the satellite data is consistently higher than in the models. For example, the maximum value of EKE in TOPEX for this region is 2072 cm2 s−2, whereas it is 1487 cm2 s−2 in FRAM and 1498 cm2 s−2 in POP. Most of the flow south of Crozet Plateau (from 35°E to 50°E) occurs between the latitudes of 47°S and 50°S in FRAM and 52°S and 56°S in POP. The EKE associated with this flow is very low in both models; that is, typically less than 100 cm2 s−2. In the TOPEX data, however, the eddy field reaches values of 800 cm2 s−2 at 50°S, which is approximately the latitude of the observed polar front. Clearly, both FRAM and POP are failing to fully resolve eddies associated with the flow in this region, although POP levels of EKE are significantly greater than in FRAM.

2) Region B: Macquarie–Ridge complex

Figure 5 shows the mean streamfunction for the Macquarie–Ridge complex in FRAM. It can be seen that there is significant southward flow in this region as well as some tight jets. The flow is clearly influenced by the upstream presence of the Campbell Plateau at 50°S, 168°E. The POP model and FRAM produce similar magnitudes of EKE in this region. The EKE distributions in the two models are also similar, although neither of them is as vigorous as in the Crozet Plateau region. As in region A, the overall level of EKE throughout the region is greater in POP than FRAM (see Figs. 6a,b). Both distributions are also significantly less than the TOPEX estimate (Fig. 6c).

3) Region C: Drake Passage

It can be seen that in FRAM the flow upstream of Drake Passage converges (Fig. 7). Beyond the passage, and slightly to the north, the model produces a very tight quasizonal jet. The flow in POP is similar to that in FRAM. However, the jet downstream of the passage undergoes significant meridional displacements before turning northward at around the same longitude as in FRAM (i.e., 305°–310°E).

The principal difference between the two models in this region is the EKE distribution. A map of FRAM’s surface-level EKE shows that most of the eddy variability occurs just upstream of the passage with very few eddies associated with the tight jet that forms downstream (Fig. 8a). POP, on the other hand, produces a strong eddy field downstream of the passage (Fig. 8b). The TOPEX EKE estimates also show a reasonably high level of variance in the geostrophic velocity in this subregion (at around 57°S, 306°E), which is similar to the POP distribution (Fig. 8c). The maximum variability from the satellite data for this region is also of a similar magnitude to that of POP, that is 874 cm2 s−2 and 744 cm2 s−2, respectively. These values are around twice the corresponding value for FRAM, which is 421 cm2 s−2.

b. FRAM kinetic energy budgets

The code used to calculate energy budgets for open regions was developed by Treguier for the CME North Atlantic Model (Treguier 1992). For a more complete description of the analysis presented here see Ivchenko et al. (1997), which includes a full regional kinetic energy analysis for the whole FRAM domain. In this section, kinetic energy budgets for the regions described in section 3a have been calculated. To understand the dynamics more fully, these regions have themselves been split into subregions, shown in Figs. 9a–c.

The energy budgets are presented in Figs. 10–13. The budgets have been split into the time-mean kinetic energy component (KEM) and the temporal variation from this mean, or eddy kinetic energy component (EKE). All terms shown have been integrated over the whole volume of the subregion, with an overbar representing the time mean and a prime representing the departure from the time mean (this is the eddy component). Here FH, FV, and FB denote horizontal, vertical, and bottom friction, respectively, and τ is the wind stress. The pressure work terms have been replaced by the buoyancy B and the pressure flux Π. The nonlinear terms have been split into those that represent advection of energy across the boundaries of the subregions (i.e., N and N′ for KEM and EKE budgets, respectively) and the internal transfer from KEM to EKE within each subregion (NR and NR) (Holland 1975; Treguier 1992; Ivchenko et al. 1997).

Analysis has also been performed for flow split into its external mode (depth averaged) and internal mode (baroclinic) components (Treguier 1992). Exchange between internal and external mode KE may occur in two ways. First, by nonlinear transfer, Nm, and second, by the topographic term, T, which describes an energy exchange caused by the bottom topography. This topographic term may be shown to be related to the energy analog of the JEBAR (Joint Effect of Baroclinicity and Relief) term (Ivchenko et al. 1997).

The most significant terms, with respect to the generation of EKE, are the eddy buoyancy term B′ and the KEM to EKE nonlinear transfer term NR. The eddy buoyancy term effectively describes a conversion between available potential (APE) and EKE. The nonlinear term may be written in the following form:
i1520-0485-29-3-328-eq1
where index λ = 1, 2 represents the two horizontal directions and index j = 1, 2, 3 represents both horizontal and vertical directions. Summation over repeated indices is implied. This term may be interpreted as the work of the Reynolds stress on the mean shear (Ivchenko et al. 1997). If NR is positive, it may also be said to represent barotropic instability. In this process energy is transferred from KEM to EKE.

The data used in this analysis is from FRAM’s 72 instantaneous datasets; that is, the end of month datasets from the last 6 years of the model run. D. P. Stevens (1996, personal communication) has compared the sampling of the monthly data taken at both 1- and 10-day intervals. One-day sampling was found to give kinetic energy levels only 1%–2% greater than both the monthly and 10-day statistics (which were virtually identical). The monthly datasets averaged over 6 years are therefore considered adequate to represent the eddy processes that occur in the model.

1) Region A: Crozet Plateau

(i) Northern branch and downstream regions

For conciseness the eddy-rich northern branch and downstream regions have been combined in Fig. 10. However, differences in the dynamics in these two regions are discussed below.

It can be seen that EKE is considerably greater than KEM in these regions. The main source of KEM is the wind stress, with the buoyancy and pressure flux acting as the main sinks. In the EKE budget the main source is the eddy buoyancy term B′. This is balanced almost exclusively by the horizontal friction, which is several times greater than in the mean budget, and to a lesser extent by the bottom friction.

The northern branch region is found to produce the greatest contribution to the source of EKE; it is responsible for about 68% of the total B′ term. The total EKE in the northern branch, however, is only slightly greater than in the downstream region. This anomaly may be explained by examining the nonlinear fluxes across the meridional boundary that separates the two regions. The eddy component of this flux represents advection of EKE from the northern branch to the downstream region. In the northern branch this eddy advection acts as a sink of EKE with a magnitude about half the value of the local B′ term. This advection of EKE acts as a source in the downstream region, although there is also a flux of EKE out of the region through the eastern meridional boundary of the downstream region. The net contribution of eddy flux in the downstream region acts as a source of EKE with a magnitude of over 30% of the B′ term. Therefore the EKE in the downstream region is due to both the B′ term and advection of eddy energy from the northern region.

The total advection of EKE across the combined northern and downstream regions boundaries represents nearly 12% of the total EKE generated; most of this is advection through the eastern meridional boundary of the downstream subregion. Nonlinear conversion from KEM to EKE in both these regions is found to be only 1% of the total EKE source terms, so evidence for barotropic instability is found to be insignificant.

Unlike the ACC as a whole, these regions have more energy in the internal mode than the external mode. The wind stress acting on the internal mode is found to be nearly three times that of the external mode. There is also strong nonlinear conversion from internal mode to external mode KE, which suggests that the inverse cascade is occurring (see Treguier 1992). The topographic term T suggests that the topography tends to make the flow more barotropic. Unlike the ACC, North ACC, and ACCB regions examined in Ivchenko et al. (1997), the eddy topographic transfers T′ in the separate northern branch and downstream regions are found to be significant. Budgets that split the EKE into the internal and external mode show that topography does influence the turbulent flow locally; that is, the eddy field in the northern branch is made more barotropic, while that in the downstream region is made more baroclinic, by the presence of the topography. The magnitudes of these topographic transfers are also significant, having around half the value of the nonlinear internal to external mode transfer Nm, which is the predominant source term for the external mode in both subregions.

(ii) Southern branch

In this region the EKE is only 18% of the KEM. Again the main source of KEM is the wind stress, which is balanced by the buoyancy and pressure flux terms acting as sinks. The main sources of EKE are the buoyancy and the nonlinear terms, one of which represents conversion from KEM to EKE, NR, whereas the other represents EKE flux over the region boundaries, N′. These terms are balanced mainly by the horizontal friction, which, by contrast with the northern and downstream regions, is smaller than in the mean balance.

The southern branch of the flow around the Crozet Plateau is considerably more barotropic than the northern branch; there is more than three times as much KE in the external mode than in the internal mode. Nonlinear exchange between the modes is much less important than it is in the eddy-rich regions.

2) Region B: Macquarie–Ridge complex

This region is found to generate a reasonably vigorous field, although it is not as strong as the Crozet Plateau region. The energy partition reflects this with 58% of the total energy in the mean component of the flow (see Fig. 11a). In the KEM balance the wind stress is by far the most important term and it is balanced mostly by the pressure flux term along with the horizontal friction and buoyancy terms. EKE is principally generated by the B′ term with some eddy pressure flux input as well. These terms are balanced by the horizontal and bottom friction.

The external mode has twice as much energy as the internal mode, making the flow far less baroclinic than in the eddy-rich Crozet Plateau regions. For the internal mode the wind stress is balanced by the sink of nonlinear conversion to external mode energy, the horizontal friction, and the pressure work term. The external mode’s main sources are the wind stress and nonlinear transfer, both of a similar magnitude balanced mostly (i.e., 75%) by a very strong horizontal friction term as well as by bottom friction and pressure work terms. Topographic exchange is from external to internal mode, which is in the opposite direction to the northern and downstream Crozet region.

The Macquarie–Ridge complex has been split into two separate subregions, that is, a west region and an east region.

In the west subregion there is about 2.5 times as much EKE in the external mode as in the internal mode (see Fig. 11b). The source terms indicate that this is because of strong EKE transfer from the internal mode by both the nonlinear transfer Nm and the influence of topography T′, which tends to make the turbulent flow more barotropic. The KEM to EKE nonlinear exchanges for each mode are represented by NB (this is to distinguish them from the total exchange, NR). It is interesting to note that although NR was found to be very small in the total Macquarie–Ridge complex, NB is found to be a significant source of EKE in the external mode for the west subregion.

The east subregion has more EKE in the internal mode than was the case for the west. About 35% of the total EKE is found in the baroclinic mode (see Fig. 11c). There are two main reasons for the differences in the partitions in these two subregions. First, in the east branch the eddy topographic term T′ acts to make the turbulence more baroclinic, and so acts as a sink for barotropic EKE. Second, the nonlinear transfer from internal to external mode EKE, Nm, is not as strong as it is in the west branch.

The most important difference between the west and east subregions is the nonlinear transfer from KEM to EKE, NB, which acts as a source of EKE in the west region but as a sink for both the internal and external mode budgets in the east region. In other words, in this part of the ACC, eddies are acting to both weaken and strengthen the mean flow.

3) Region C: Drake Passage region

(i) Upstream subregion

There is three times as much KEM as EKE in this region, which has much less EKE than the regions described above (see Fig. 12). The mean components include the usual balance between wind stress, buoyancy, and horizontal friction but also include a strong nonlinear advection of mean KE across the boundaries out of the regions; this term has a magnitude 34% of the wind stress term. In the EKE budget, the B′ term is again the principal source of energy; however, the KEM to EKE nonlinear exchange is more significant in this region than it is in the other eddy-rich regions, representing nearly 7% of the buoyancy term.

The flow in the upstream region is found to be the most barotropic of the eddy-rich regions examined in the ACC, with nearly three times as much energy in the external mode than the internal mode. Of principal interest among the energy transfer terms in the internal/external mode partition are the nonlinear terms. Like the other eddy-rich ACC subregions, there is significant nonlinear exchange from internal to external mode energy. For the external mode balance this term acts as a source with a magnitude of 24% of the wind stress term. The other important nonlinear term is the advection across the region’s boundaries. The topographic transfer term indicates an energy transfer from internal to external mode, as it did for the Crozet Plateau northern branch and downstream region, although here the magnitude is more than twice the value found in that region. The eddy topographic term T′ acts in the opposite direction and is a significant source of internal mode EKE, representing about 22% of the main EKE source.

(ii) Northern branch

The KE of the flow resides mostly in the mean component with the eddy component representing less than 4% of the total energy (Fig. 13). In the KEM balance the wind stress, nonlinear transfer, and pressure fluxes are the main sources with the horizontal friction, buoyancy, and bottom friction the main sinks. Horizontal friction is, along with the buoyancy term, the most important sink, unlike the other ACC regions considered, where the mean horizontal friction is not so important.

The main sources of EKE are the buoyancy term and also a significant nonlinear flux advected in from the upstream region. As well as horizontal friction the sink of eddy energy includes a component of nonlinear transfer from EKE to KEM, which represents tightening of the jet by Reynolds stress divergence. The only other ACC subregion found to definitely exhibit this process is the east region of the Macquarie–Ridge complex.

The internal/external mode partition shows that the flow in this region is highly barotropic, with 89% of the total energy in the external mode. This is principally because of the wind stress, which does almost as much work on the external mode as it does on the internal mode. The topographic term suggests a conversion due to the topography from external mode to internal mode, which is in the opposite direction to the upstream region. Its magnitude, however, is only 10% of the upstream value. The eddy topographic term T′ is in the opposite direction and represents the main source of external mode EKE.

For completeness we also examined the southern branch, but because there is very little flow in this region, we found nothing that was dynamically interesting.

c. Instability analysis

The instability analysis presented here is based on that of Beckman (1988) and A. M. Treguier (1996, personal communication). This method is used to assess whether baroclinic instability is responsible for the generation of eddies in various regions within the Southern Ocean in both the FRAM and POP model solutions.

Baroclinic instability is examined by calculating the unstable modes of the zonal shear ur(z), which is a domain-averaged zonal velocity only dependent on depth. To do this, the eigenvalue problem, described by Beckman (1988), is solved for the spatially and time-averaged shear of the zonal velocity ur(z) and the corresponding mean density profile, represented by the Brunt–Väisälä frequency, N2(z). This analysis has been performed for the subregions of the ACC investigated in this study. Table 1 shows the regions investigated. Note, FRAM and POP sometimes have significantly different coordinates for the region described. This simply reflects the difference in position of the ACC jets in the two models. For example, the flow around the south of Crozet Plateau is approximately 6° farther south in POP compared with FRAM. Only quasi-zonal flows have been considered in this analysis; that is, averaged values of meridional velocity υ below the surface Ekman layer are typically an order of magnitude less than the zonal velocity u. Furthermore, the zonal shear of the flow is assumed to be uniform with latitude.

In all the regions considered, the flow has been found to be baroclinically unstable. In FRAM the growth rate ranges from 12.6 to 65.0 day−1, and in POP from 11.7 to 311.6 day−1. In the majority of regions the most unstable wavelengths are marginally resolved by the zonal grid spacing. Maximum growth rates are found to occur on scales from approximately 1.6 to 3.6 times the first Rossby radius in FRAM and from 1.3 to 7.1 times the first Rossby radius in the POP analysis.

In order to compare the instability analysis with the actual instabilities produced by each of the models, the KEM and EKE have been calculated by depth averaging over each subregion. These values are shown in Table 2. The results of the instability analysis are shown in Table 3, which gives the maximum growth rates along with the corresponding wavelength at which the predicted growth rate occurs. This analysis has been carried out both with and without horizontal friction.

First let us consider the results of the experiments that include horizontal friction. By comparing Tables 2 and 3 it can be seen that there is a reasonable connection between the maximum growth rate and the amount of EKE produced by the respective models; that is, the fastest growth rates tend to correspond to highest values of EKE. This suggests that baroclinic instability is the dominant eddy-generating mechanism in most of the eddy-rich regions considered here. Further insight into the differences between the two models may be obtained by comparing and contrasting the instability analysis.

Analysis of the flow upstream of Crozet Plateau gives unstable waves with fast growth rates in both models. Despite this, EKE levels actually produced by the models are only moderate compared with other regions with similar growth rates; for example, the flow around the north of Crozet Plateau. Furthermore, studies of satellite data in this region show that the EKE field remains vigorous as the flow moves between the Agulhas return current to the Crozet Plateau and beyond (e.g., Quartly and Srokosz 1993). There is no evidence to suggest that this lack of EKE is due to insufficient model resolution in this region. Indeed, the wavelength of the most unstable wave is the longest of all regions considered in POP, and second longest in FRAM. It seems reasonable to suggest that for both models, topography is responsible for triggering the particularly vigorous eddy field that occurs to the north and downstream of Crozet Plateau. The lack of eddies in the flow south of Crozet Plateau is consistent with the results of the instability analysis. Each model gives its second slowest growth rate in this region.

An interesting difference between the two model solutions is in the region downstream of the Crozet Plateau. In FRAM this region has the slowest growth rate found in this study, yet still has a considerable amount of EKE. This anomaly may be partly explained by a regional kinetic energy budget, which shows that more than 30% of this EKE is advected in from upstream (a much higher proportion than in the other regions). The POP downstream region has one of the highest EKE densities and the fastest growth rate of all regions considered in this experiment. This is again consistent with the view that eddies in this region are generated by baroclinic instability.

Finally, the results of the analysis around Drake Passage are worth comment. In FRAM the flow upstream and just to the northeast of the passage both have very similar growth rates that are reasonably fast. A significant difference between the two regions is that the EKE density in the upstream flow is twice that of the northeastern flow. One reason why the flow northeast of Drake Passage remains relatively stable in FRAM, despite the predicted instability, is that the wavelength at which instability is most likely to occur, λmax, is only resolved by three zonal grid points. Furthermore, the local first baroclinic Rossby radius is only just over one grid box in length. This strongly suggests that the stability of the flow downstream of Drake Passage is due to a lack of resolution in FRAM.

By way of contrast, both POP and TOPEX distributions give vigorous eddy distributions downstream of Drake Passage. The instability analysis of POP in this region, however, gives a very slow growth rate (i.e., 312 day−1). One possible explanation for this is that downstream of Drake Passage barotropic instability is the dominant mechanism. This may be expected since the jet produced by POP is very tight.

The instability analysis has also been performed without horizontal friction, to see how this friction affects the instabilities produced. As can be seen from Table 3, the maximum growth rates are faster when horizontal friction is dropped from the model analysis. In the FRAM analysis the values of maximum growth rates increase by between 1.3 and 3.0 times. POP results are similar, with most regions experiencing an increase of growth rate by between 1.2 and 2.9 times. The exception to this is the region east of Drake Passage, whose growth rate is 28.6 times faster when horizontal friction is removed. For both models, the fastest growth rates are least affected by the loss of friction, while the slowest are most affected.

4. Zonally and streamwise-averaged flow

Zonal averaging is a classical tool for understanding the dynamical processes occuring in zonal flows; this tool is usually used in the atmospheric sciences. In ocean dynamics such averages are not usually helpful because of the ocean boundaries that block the flow. The Southern Ocean is the only domain in the World Ocean where at the latitudes of Drake Passage there is an unbounded zonal belt and consequently zonal averaging can provide real insights.

Despite these advantages, zonal averaging in the ACCB misses a large part of the flow. For example 80% of the ACC’s EKE is generated on the northern flank of the current, outside the ACCB (Ivchenko et al. 1997). It is therefore interesting to take averages along time-mean streamlines (or sea surface height isolines). The ACCB averaging is presented in section 4a, with the streamline averaging presented in section 4b.

a. The zonal-averaged flow (ACCB)

The zonally averaged zonal velocity [u]zon has three peaks in both FRAM and POP (see Figs. 14a,b). Hereafter overbar represents the time average and [ · ]zon means zonal averaging. The zonal and meridional components of the velocity are u and υ, respectively. Here [u]zon is always positive above topographic obstacles. The highest values occur in the northern flank and are about 9 cm s−1 in the top layer in FRAM and 10 cm s−1 in POP; there is an equivalent-barotropic distribution of the velocity (i.e., it is similar with depth) and values decrease downward. The main distribution of the flow is broader in FRAM; the positions of the jet cores are slightly different, as well.

The correlation []zon can be split into three terms:
i1520-0485-29-3-328-e1
Here the dagger marks the transient eddy components, that is,
uuu
and u* corresponds to the standing eddy components, that is,
u[u]zonu

The first term on the rhs of expression (1) corresponds to the mean flow (the so-called overturning term), the second term describes the standing eddy Reynolds stress, and the third corresponds to transient eddies.

In both experiments the overturning term is negligible in the intermediate layers, because of the very small mean ageostrophic velocity [u]zon. The most important term is the standing-eddy Reynolds stress. This is not surprising because the ACC moves away from a zonal path in many places.

The first striking result in POP is that all the components of the Reynolds stress are predominantly positive (except for a very small overturning term). This distribution is associated with the flux of the eastward momentum equatorward. Another important feature is the dramatic decrease in the magnitude of the Reynolds stress components toward the north; the total stress, both standing and transient eddy components, drops to large negative values (Fig. 15). We suggest that for the standing eddy component this happens because of the generally poleward component of the mean flow on the northern flank, especially in the Pacific and Atlantic sectors of the ACCB. This is not the case in the Indian sector where there is also a significant equatorward component in the mean flow. Particularly strong equatorward flow also occurs just to the east of Drake Passage. However, for the northern ACCB as a whole the poleward component dominates. The negative values of the transient eddy component are less clear. Note, however, that almost everywhere, excluding a rather small northern area, the transient-eddy Reynolds stress is positive.

In both models the main zonal momentum balance in the intermediate layers (above topographic obstacles) occurs between the divergence of the Reynolds stress and the Coriolis term. In this balance the overturning term is negligible; both standing and transient eddy components are significant, although the standing eddy component is the greater. In both experiments the positions of the three main jets are strongly connected with the high positive values of the divergence of the transient eddy component of the Reynolds stress.

In the ACCB transient-eddy momentum flux divergence accelerates the zonal flow for both models. However, the overall effect of the standing and total Reynolds stress components, calculated by meridionally integrating the divergence of the respective stresses over the whole zonal belt, have opposite signs in the two experiments: acceleration in POP and deceleration in FRAM. This may be due to the different topographic fields in the two models, which could influence the extension of the main ACC across the open zonal boundaries of the ACCB and hence lead to different standing-eddy components. Because the magnitude of the standing eddy component is greater than that of the transient eddy component, the distribution of the former plays a more important role in the total component of the Reynolds stress.

The KEM and zonal momentum distributions are similar, with both having three peaks. The EKE distribution, by contrast, is quite smooth, without peaks. We suggest that this happens because of strong eddy mixing. The standing eddy KE distribution (not shown) is between the KEM and the EKE: there are peaks, but they are not as prominent as in the mean flow case. The highest values correspond to the EKE and the lowest to the KEM.

b. The streamwise-averaged flow (ACCP)

To analyze the flow in a streamwise sense we have taken integration paths that are approximately streamlines. In the case of FRAM it is most convenient to take the barotropic streamfunction. For POP we have used sea-surface height contours. The difference between these paths and streamlines is small, the average tangential velocity being of order 103–104 times larger than the average normal velocity (above topographic obstacles). However it must be remembered that there is some change in flow direction with depth. This leads to a nonzero standing eddy component, which is discussed below.

Tangential velocities, averaged along these paths, are much larger than those that have been zonally averaged. These values are also always positive above topographic obstacles. In FRAM there are three main cores: near ψ = 30 Sv, 80 Sv, and 150 Sv. The distribution in the POP model is smoother, but not as smooth as in the Semtner–Chervin model (see Gille 1995). Both experiments (FRAM and POP) show the equivalent-barotropic distribution of tangential velocity [υtang] (see Figs. 16a,b). (Here [ · ] means the averaging along time-mean barotropic streamfunctions for FRAM and time-averaged isolines of the sea surface height for POP.) The surface tangential velocities ([υtang]) calculated from Geosat altimetry (Gille 1995) are found to be much higher than the corresponding values for FRAM and lower than in the Semtner–Chervin model results. The POP results are found to be in reasonable agreement. For example, the highest value is 15 cm s−1 in FRAM, about 27 cm s−1 in the Semtner–Chervin model, and 20 cm s−1 in POP, whereas Geosat gives a value of about 23 cm s−1. The velocity peaks, associated with the SubAntarctic and Polar Fronts, are more distinct in the satellite altimeter profile than in the model profiles.

FRAM produces flow that is more barotropic than in POP. For example, in the top 1000 m POP’s averaged tangential velocity is greater than FRAM’s, but at a depth of between 1500 and 2000 m, and deeper FRAM’s velocity is greater. The mean normal velocity, [υnorm], generally has a poleward direction in intermediate levels.

The transient-eddy Reynolds stress is positive everywhere in both experiments and therefore corresponds to the equatorward transport of the eastward momentum (see Figs. 17a,b). In POP, the transient Reynolds stress is higher than in FRAM (by about a factor of 2 or 3), presumably because of the better resolution. There are large negative values of the standing-eddy stress component at the northern part of the area. This component is positive almost everywhere in the central and southern part in FRAM, but still negative in the same area in POP. We suggest that such a difference in the contribution of the standing eddy component is strongly connected with the differences in topography. The total [υtangυnorm] is higher than the standing Reynolds stresses everywhere because of the positive contribution from the transient Reynolds’ stress. In the southern flank of the ACC, however, FRAM and POP give very different results for the standing component and the total stress, with positive values in FRAM and negative values in POP.

In both models’ top layer there is a strong equatorward Ekman velocity; so the mean flux, [υtang][υnorm], is quite large and positive. In the second layer the mean normal velocity, [υnorm], is much less than that in the top layer, but much higher than the velocity beneath. So, in the second layer [υtang][υnorm] is positive almost everywhere and comparable to the other components. Beneath the second layer this term is much smaller than other components.

To assess the impact of the Reynolds stresses on the flow we need to calculate the divergence of these stresses. This has been done for both models by integrating along time-mean streamlines for FRAM and sea-surface height isolines for POP. The results show that the transient component of the divergence of the Reynolds stresses provide a net drag on the flow in both models. However, the total and time-mean components accelerate the ACC in FRAM but decelerate it in POP (see Ivchenko et al. 1996).

The level of the total KE in FRAM is about two to three times lower than in POP in the top layers (see Figs. 18a,b). In FRAM the highest input to the total KE comes from the standing eddies and the lowest comes from the transient eddies. In POP’s top layers the highest contribution to the total KE comes from the transient eddies with the lowest from the KE of the mean flow. The input by these three components looks more or less equal in the lower layers.

Similarly, in the zonally averaged case FRAM produces a more barotropic distribution of the total kinetic energy than POP. At a depth of 2000 m both maximum and averaged values of the total kinetic energy are higher in FRAM.

The streamline-averaged EKE in FRAM’s top layer is at least four times smaller than that from Geosat (Gille 1995). POP’s value of averaged EKE is considerably higher; that is within 80%–85% of that estimated from Geosat. In areas with strong large-scale topographic features, however, FRAM and POP produce values of EKE that are not very different (see regional analysis in section 3 and discussion in section 5).

Gille (1995) has noted that neither FRAM nor Semtner–Chervin models produce the peak in EKE to the north of the central ACC (the 0.1-m height contour in her figure). The POP model has simulated this peak (figure not shown), although it appears to occur slightly to the north of the corresponding altimeter distribution.

5. Discussion and conclusions

This study has examined mesoscale variability in two near-eddy-resolving primitive equation models (namely FRAM and POP) in order to understand more completely the part eddies play in the dynamics of the ACC. One major issue is the transport of the ACC in Drake Passage and what controls this transport.

The transport of the ACC as estimated from the ISOS dataset is about 130 Sv (Nowlin and Klinck 1986). Recent observations at Drake Passage have shown substantially higher mass transport, however. Cunningham et al. (1995) found the baroclinic flux (zero reference geostrophic velocity at the bottom) to be 144 Sv in 1994. The overestimation of the transport in the ACC has been regarded as endemic in primitive equation models (Stevens and Ivchenko 1997). For instance, the global eddy-resolving model of Semtner and Chervin (1988) has a transport of 190 Sv through Drake Passage, while FRAM has a transport of 185 Sv (The FRAM Group 1991; Webb et al. 1991). Grose et al. (1995) have shown that the International Southern Ocean Study (ISOS) current meter array would underestimate the transport through Drake Passage in FRAM. In the POP model, the mean transport across the passage is 134 Sv (for 5-yr averaging) and 136 Sv for 10-yr averaging (Maltrud et al. 1997, manuscript submitted to J. Geophys. Res.). These results are even more surprising because the wind stress in POP over the ACC area is higher than in FRAM. The zonally and streamwise-averaged wind stress of POP are both 15%–20% higher than that of FRAM. Why, in spite of this, is the ACC transport in POP substantially less than that in the FRAM and Semtner–Chervin (1988) runs? Two possible reasons are

  • different horizontal resolution. At Drake Passage latitudes the POP resolution is about 15 km, compared with 27 km in FRAM. The higher resolution produces a more energetic eddy field, which could lower the mean transport.

  • different topography. The FRAM topography has been smoothed, whereas the POP topography has not. Smoothing the topography could result in less obstruction to the barotropic flow.

We are unable to give a definitive answer because the two models differ in a number of aspects.

Like Wilkin and Morrow (1994) we find that the geographical distribution of eddy variability agrees well with that observed from satellite altimetry (in this case TOPEX). In FRAM’s top layers the EKE levels are much lower than those observed. Stevens and Killworth (1992) have shown that for FRAM, the EKE is at best only 25% of observational estimates. Ivchenko et al. (1997) suggest that this deficit of EKE occurs as a result of the high lateral friction, which decreases the growth rates of the most unstable waves. This high friction can only be made smaller by using a finer horizontal resolution. Ivchenko et al. (1997) suggest that a grid spacing of 10–15 km or finer is necessary to resolve the most unstable waves.

The resolution of POP approaches this value (e.g., POP has a grid spacing of 15.6 km at 60°S). Indeed, averaged along constant sea surface height the EKE of POP is close to that estimated from Geosat and at least three times greater than in FRAM. (This difference is even more significant for the whole ocean south of the ACC where FRAM’s horizontal grid spacing is clearly failing to resolve the small internal Rossby radius at these latitudes.)

It is also interesting to note that in POP, with its better horizontal resolution, the greatest energy contribution to the total KE comes from the transient eddy component, whereas in FRAM the highest input comes from the standing eddy component. Beckman et al. (1994) also find a substantial increase in EKE with increased model resolution for the North Atlantic.

The higher-frequency wind forcing in POP (3-day means) versus FRAM (monthly means) evidently does not explain the higher EKE values seen in POP. Figure 19 shows the zonally averaged EKE at the second model level (37.5 m) using 8-yr averages from the two simulations: one with monthly mean winds (POP5), and the other with 3-day wind (POP7). The agreement is good in spite of the fact that the two simulations started from different initial conditions. This indicates that the mesoscale eddy field produced in response to the wind forcing is quite robust, as was found in other studies (Maltrud et al. 1997, manuscript submitted to J. Geophys. Res.). The EKE field in the surface layer (not shown) is, in fact, higher in POP7 with the high-frequency winds, but in this layer the flow can be dominated by Ekman balance rather than geostrophic balance found to occur in the subsurface layers. Thus the high-frequency winds significantly affect EKE in the Ekman layer, but not the subsurface geostrophically balanced mesoscale eddy field.

Both standing and transient eddy components of the Reynolds stress distribution have been calculated for the two models. This has been carried out using both zonally averaged and streamwise-averaged flow. All of the components of the Reynolds stress for POP in the zonally averaged case were found to be predominantly positive. An interesting result is that the transient-eddy Reynolds stresses are positive almost everywhere for both types of averaging (i.e., zonal and streamwise) and for both models. Positive Reynolds stresses are associated with an equatorward eddy transport of eastward momentum. The standing eddy component of the Reynolds stress has both signs and is strongly dependent on the topography.

Bryden (1983) has proposed that baroclinic instability is the main mechanism responsible for the generation of eddies in the Southern Ocean, particularly in the western boundary currents and the major fronts of the ACC. This view is reinforced by an energy analysis of FRAM, which shows that B′ is the main source of EKE. This may be interpreted as EKE converted from APE (Ivchenko et al. 1997). In order to further understand the energy cycle occuring in FRAM the transfer from mean APE (PEM) to eddy APE (EPE) has also been estimated following the method of Böning and Budich (1992). This term, A′, was found to be greater than B′ for all the subregions described in section 3b, except for the relatively stable flow south of Crozet Plateau. This is consistent with the classical interpretation of baroclinic instability as the generation of EKE from PEM.

Instability analysis by Ivchenko et al. (1997) showed that all regions within FRAM’s ACC may become baroclinically unstable with typical growth rate of 50 day−1. In this study, a similar analysis has been performed on selected quasi-zonal jets of particular interest in both FRAM and POP. In these regions the results of the instability analysis are reasonably similar in both models. An important exception to this is Drake Passage, which helps to highlight some of the differences between FRAM and POP. The jet that forms just downstream of Drake Passage (called Drake Passage Northern region) has 12 times more EKE associated with it in POP than in FRAM. Instability analysis shows that in FRAM the growth rate for the most unstable modes are similar to those found for the upstream region where there was reasonable EKE generation by baroclinic instability.

One reason for this difference between models is that the predicted wavelength at which the most unstable mode grows, λmax is resolved by only three zonal grid points in FRAM (whereas in the Macquarie–Ridge complex, for example, λmax is resolved by more than eight grid points). Another possible reason is suggested by the regional kinetic energy budget calculated for selected regions within the ACC (section 3b). It shows that in the Drake Passage Northern region nonlinear transfer represented an exchange from EKE to KEM. In other words eddies act to tighten the jet (the “negative viscosity” effect).

The results of the instability analysis of POP downstream of Drake Passage are surprising at first sight. This region, which produces a vigorous eddy field gives a growth rate more than an order of magnitude slower than the other eddy-rich regions considered. One possible explanation for this is that the eddies are generated by a nonlinear transfer from KEM to EKE, that is, by barotropic instability. This mechanism would be expected in this region because of the strong horizontal shear in the zonal velocities. However, in order to determine the extent to which this is an important mechanism, a regional kinetic energy budget would have to be carried out on the POP data.

An important question is are eddies a source or a sink for the quasi-zonal mean flow? We found that the transient eddies accelerate the zonal flow (ACCB) but decelerate the flow in streamwise coordinates (ACCP), in both experiments. There is no theoretical reason why transients cannot act in either direction. However, it is unclear why they act differently in the ACCB and ACCP and this question requires further study.

Comparing and contrasting the results from the two eddy-resolving models, FRAM and POP, has led to some important insights into the controlling factors of the mean and eddy transports in the Southern Ocean. Despite the many differences in the configuration of the two models we have been able to give some explanation for the similarities and differences between them. We have not, however, been able to give definitive answers to many of the questions raised. To do this would require a carefully constructed series of sensitivity experiments, using both global and regional models, to delineate the various factors influencing the flow.

Acknowledgments

We gratefully acknowledge the help of Dr. A. M. Treguier, who supplied us with her software for the instability analysis and for the regional kinetic energy budget. Dr. P. Y. Le Traon provided us with his TOPEX data. We gratefully acknowledge the help and support of the FRAM team in providing the data from the numerical model experiment. We had useful discussions with Dr. N. C. Wells and Dr. D. Webb. We are also grateful to our anonymous reviewers for providing useful criticisms, which significantly improved the structure and presentation of this paper. S. Best was supported by a NERC Studentship. V. O. Ivchenko was supported by the NERC under Grant GST/02/817. R. Smith and R. Malone acknowledge support from the U.S. DOE CHAMMP program.

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  • Pacanowski, R. C., and S. G. H. Philander, 1981: Parameterization of vertical mixing in numerical models of tropical oceans. J. Phys. Oceanogr.,11, 1443–1451.

  • Park, Y. H., L. Gamberoni, and E. Charriand, 1993: Frontal structure, water masses and circulation in the Crozet Basin. J. Geophys. Res.,98, 12 361–12 385.

  • Quartly, G. D., and M. A. Srokosz, 1993: Seasonal variations in the region of the Agulhas Retroflection: Studies with GEOSAT and FRAM. J. Phys. Oceanogr.,23, 2107–2124.

  • Sarukhanian, E. I., and N. P. Smirnoff, 1986: Water Masses and Circulation of the Southern Ocean. Hydrometeorologisher Publ., Leningrad, 288 pp.

  • Semtner, A. J., and R. M. Chervin, 1988: A simulation of the Global Ocean circulation with resolved eddies. J. Geophys. Res.,93, 15 502–15 522.

  • ——, and ——, 1992: Ocean general circulation from a global eddy-resolving model. J. Geophys. Res.,97, 5493–5550.

  • Smith, R. D., J. K. Dukowicz, and R. C. Malone, 1992: Parallel ocean general circulation modeling. Physica D,60, 38–61.

  • Stevens, D. P., 1990: On open boundary conditions for three-dimensional primitive equation ocean circulation models. Geophys. Astrophys. Fluid Dyn.,51 (1–4), 103–133.

  • ——, and P. D. Killworth, 1992: The distribution of kinetic energy in the Southern Ocean: A comparison between observations and an eddy resolving general circulation model. Philos. Trans. Roy. Soc. London,338B, 251–257.

  • ——, and V. O. Ivchenko, 1997: The zonal momentum balance in an eddy-resolving general-circulation model of the Southern Ocean. Quart. J. Roy. Meteor. Soc.,123, 929–951.

  • Toggweiler, J. R., and B. Samuels, 1995: Effect of Drake Passage on the global thermohaline circulation. Deep-Sea Res.,42, 477–500.

  • Treguier, A. M., 1992: Kinetic energy analysis of an eddy resolving, primitive equation model of the North Atlantic. J. Geophys. Res.,97, 687–701.

  • ——, and J. C. McWilliams, 1990: Topographic influences on wind-driven, stratified flow in a β-plane channel: An idealized model for the Antarctic Circumpolar Current. J. Phys. Oceanogr.,20, 321–343.

  • Webb, D. J., P. D. Killworth, A. C. Coward, and S. R. Thompson, 1991: The FRAM Atlas of the Southern Ocean. Natural Environment Research Council, 67 pp.

  • Wilkin, J. L., and R. A. Morrow, 1994: Eddy kinetic energy and momentum flux in the Southern Ocean: Comparison of a global eddy-resolving model with altimeter, drifter, and current-meter data. J. Geophys. Res.,99, 7903–7916.

  • Wolff, J.-O., E. Maier-Reimer, and D. J. Olbers, 1991: Wind-driven flow over topography in a zonal β-plane channel: A quasigeostrophic model of the Antarctic Circumpolar Current. J. Phys. Oceanogr.,21, 236–264.

Fig. 1.
Fig. 1.

(a) FRAM’s eddy kinetic energy in the top model layer (10.3 m), calculated over the last 6 years of the run. Contours are cm2 s−2 (after Ivchenko et al. 1997). (b) POP’s eddy kinetic energy in the top model layer (12.5 m). Contours are cm2 s−2. (c) Variance of the geostrophic velocity from TOPEX data (courtesy of P. Y. Le Traon). Contours are cm2 s−2 (after Ivchenko et al. 1997).

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 2.
Fig. 2.

The ACC regions: boxes A–C show the flow around Crozet Plateau, south of Australia (Macquarie–Ridge Complex), and Drake Passage, respectively. The contours show FRAM’s 6-yr time-mean streamfunction (top to bottom 10, 60, 130, and 180 Sv) to indicate the path of the ACC.

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 3.
Fig. 3.

FRAM time-mean streamfunction for the Crozet Plateau region. Contours in Sv.

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 4.
Fig. 4.

The EKE of the surface level for the Crozet Plateau region. Units are in cm2 s−2. (a) FRAM energy (depth 10.3 m). (b) POP energy (depth 12.5 m). (c) TOPEX velocity variances (courtesy P. Y. Le Traon).

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 5.
Fig. 5.

FRAM time-mean streamfunction for Macquarie–Ridge complex. Contours in Sverdrups.

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 6.
Fig. 6.

The EKE of the surface level for the Macquarie–Ridge complex. Units are in cm2 s−2. (a) FRAM energy (depth 10.3 m). (b) POP energy (depth 12.5 m). (c) TOPEX velocity variances (courtesy P. Y. Le Traon).

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 7.
Fig. 7.

FRAM time-mean streamfunction for Drake Passage region. Contours in Sverdrups.

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 8.
Fig. 8.

The EKE of the surface level for the Drake Passage region. Units are in cm2 s−2. (a) FRAM energy (depth 10.3 m). (b) POP energy (depth 12.5 m). (c) TOPEX velocity variances (courtesy P. Y. Le Traon).

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 9.
Fig. 9.

Partition of subregions. Streamlines indicate the time-mean flow. (a) The Crozet Plateau region, (b) Macquarie–Ridge complex, and (c) Drake Passage region.

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 10.
Fig. 10.

Time-mean and EKE balances for the Crozet Plateau northern and downstream regions. Units are cm2 s−2 for energy levels and 10−7 cm2 s−3 for energy transfer terms.

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 11.
Fig. 11.

(a) Time-mean and EKE split for the combined Macquarie–Ridge complex. Units are cm2 s−2 for energy levels and 10−7 cm2 s−3 for energy transfer terms. (b) Internal mode and external mode split for the EKE in the west subregion of Macquarie–Ridge complex. Units are cm2 s−2 for energy levels and 10−8 cm2 s−3 for energy transfer terms. (c) As for (b) except for east subregion of Macquarie–Ridge complex.

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 12.
Fig. 12.

Time-mean and EKE split for the upstream Drake Passage region. Units are cm2 s−2 for energy levels and 10−7 cm2 s−3 for energy transfer terms.

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 13.
Fig. 13.

Time-mean and EKE split for the northern branch of the Drake Passage region. Units are cm2 s−2 for energy levels and 10−7 cm2 s−3 for energy transfer terms.

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 14.
Fig. 14.

The averaged zonal velocity [u]zon in cm s−1. The velocity decreases monotonically with depth. The horizontal axis is latitude in °S. (a) For FRAM [u]zon at levels k = 1–17 (10.3–1945 m) (after Stevens and Ivchenko 1997) and (b) For POP [u]zon at levels k = 1–14 (12.5–1975 m).

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 15.
Fig. 15.

POP’s zonally averaged Reynolds stress at level 3 (depth 62.5 m). Lines 1, 2, 3, 4 represent the total stress ([]zon), standing eddy ([u*υ*]zon), overturning ([u]zon[υ]zon) and transient eddy ([uυ†]zon) components, respectively. The units of stress are cm2 s−2. The horizontal axis is latitude in °S.

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 16.
Fig. 16.

(a) Alongstreamline average of the along streamline component of velocity of the model ACC, for each of the upper 17 FRAM levels as a function of streamline, (cm s−1). The current decreases with depth from level 1 (10.3 m) to level 17 (1945 m). (b) Along constant sea surface height averaged tangential velocity, for each of the upper 14 POP model levels (cm s−1). The current decreases with depth from level 1 (12.5 m) to level 14 (1975 m). The horizontal axis corresponds to the negative surface height in cm.

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 17.
Fig. 17.

(a) Alongstreamline averaged Reynolds stress at level 2 in FRAM (32.5 m) and its components. Lines 1, 2, 3, 4 represent total, standing eddy, mean (overturning), and transient components, respectively. The units are Sverdrups and cm2 s−2 (after Ivchenko et al. 1996). (b) Along constant sea surface height averaged Reynolds stress at level 2 in POP (37.5 m) and its components. Lines 1, 2, 3, 4 represent total, standing eddy, mean (overturning), and transient components, respectively. The units are cm2 s−2. The horizontal axis corresponds to the negative surface height in cm.

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 18.
Fig. 18.

(a) Alongstreamline average of the total kinetic energy for the ACC in FRAM’s upper 17 levels, as a function of streamline. The energy decreases with depth from level 1 (10.15 m) to level 17 (1945 m). (b) The along constant sea surface height average of the total kinetic energy of POP’s ACC, for each of the upper 14 model levels, as a function of sea surface height. The units are cm2 s−2. The horizontal axis corresponds to the negative surface height in cm. The energy decreases with depth from level 1 (12.5 m) to level 14 (1975 m).

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Fig. 19.
Fig. 19.

Zonally averaged EKE in the second layer (37.5 m) for the POP. The solid line corresponds to POP5 and the the dashed line to POP7.

Citation: Journal of Physical Oceanography 29, 3; 10.1175/1520-0485(1999)029<0328:EINMOT>2.0.CO;2

Table 1.

Model region boundaries for FRAM and POP models.

Table 1.
Table 2.

Energy densities within the seven regions in the FRAM and POP models.

Table 2.
Table 3.

Transport current analysis with and without friction for the FRAM and POP models.

Table 3.
Save
  • Barnier, B., L. Siefridt, and P. Marchesiello, 1995: Thermal forcing for a global ocean circulation model using a three-year climatology of ECMWF analysis. J. Mar. Syst.,6, 363–380.

  • Beckmann, A., 1988: Vertical structure of midlatitude mesoscale instabilities. J. Phys. Oceanogr.,18, 1354–1371.

  • ——, C. W. Böning, C. Köberle, and J. Willebrand, 1994: Effects of increased horizontal resolution in a simulation of the North Atlantic Ocean. J. Phys. Oceanogr.,24, 326–344.

  • Böning, C., and R. G. Budich, 1992: Eddy dynamics in a primitive equation model: Sensitivity to horizontal resolution and friction. J. Phys. Oceanogr.,22, 361–381.

  • Bryden, H. L., 1983: The Southern Ocean. Eddies in Marine Science, A. R. Robinson, Ed., Springer, 265–277.

  • Cunningham, S. A., S. G. Alderson, and B. A. King, 1995: Inter-annual variations in the mass flux of the Antarctic Circumpolar Current at Drake Passage on WOCE repeat hydrography section, SR1. Abstracts, 221st General Assembly of the Int. Assoc. for the Physical Sciences of the Oceans (IAPSO), Honolulu, HI, 25.

  • Dukowicz, J. K., and R. D. Smith, 1994: Implicit free-surface method for the Bryan–Cox–Semtner ocean model. J. Geophys. Res.,99, 7991–8014.

  • ——, ——, and R. C. Malone, 1993: A reformulation and implementation of the Bryan–Cox–Semtner ocean model on the Connection Machine. J. Atmos. Oceanic Technol.,10, 196–208.

  • The FRAM Group, 1991: Initial results from a fine resolution model of the Southern Ocean. Eos, Trans. Amer. Geophys. Union,72, 174–175.

  • Gille, S. T., 1995: Dynamics of the Antarctic Circumpolar Current: Evidence for topographic effects from altimeter data and numerical model output. Ph.D. thesis, Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 217 pp.

  • Gouretski, V. V., A. I. Danilov, V. O. Ivchenko, and A. V. Klepikov, 1987: Modelling of the Southern Ocean Circulation. Hydrometeorologisher, Leningrad, 200 pp.

  • Grose, T. J., J. A. Johnson, and G. R. Bigg, 1995: A comparison between the FRAM (Fine Resolution Antarctic Model) results and observations in the Drake Passage. Deep-Sea Res.,42, 365–388.

  • Hellerman, S., and M. Rosenstein, 1983: Normal monthly wind stress over the World Ocean with error estimates. J. Phys. Oceanogr.,13, 1093–1104.

  • Holland, W. R., 1975: Energetics of baroclinic oceans. Numerical Models of Ocean Circulation, National Academy Press, 168–177.

  • Ivchenko, V. O., K. J. Richards, and D. P. Stevens, 1996: The dynamics of the Antarctic Circumpolar Current. J. Phys. Oceanogr.,26, 753–774.

  • ——, A. M. Treguier, and S. E. Best, 1997: A kinetic energy budget and internal instabilities in the Fine Resolution Antarctic Model. J. Phys. Oceanogr.,27, 5–22.

  • Johnson, G. C., and H. L. Bryden, 1989: On the size of the Antarctic Circumpolar Current. Deep-Sea Res.,36, 39–53.

  • Killworth, P. K., and M. M. Nanneh, 1994: On the isopycnal momentum budget of the Antarctic Circumpolar Current in the Fine Resolution Antarctic Model. J. Phys. Oceanogr.,24, 1201–1223.

  • Le Traon, P. Y., J. Stum, J. Dorandeu, and P. Gaspar, 1994: Global statistical analysis of TOPEX and POSEIDON data. J. Geophys. Res.,99 (C12), 24 619–24 631.

  • Levitus, S., 1982: Climatological Atlas of the World Ocean. NOAA Prof. Paper No. 13, U.S. Govt. Printing office, 173 pp.

  • Marshall, J., D. Olbers, H. Ross, and D. Wolf-Gladrow, 1993: Potential vorticity constraints on the dynamics and hydrography of the Southern Ocean. J. Phys. Oceanogr.,23, 465–487.

  • McWilliams, J. C., W. R. Holland, and J. S. Chow, 1978: A description of numerical Antarctic Circumpolar Currents. Dyn. Atmos. Oceans.,2, 213–291.

  • Munk, W. H., and E. Palmén, 1951: Note on the dynamics of the Antarctic Circumpolar Current. Tellus,3, 53–55.

  • Nowlin, W. D., Jr, and J. M. Klinck, 1986: The physics of the Antarctic Circumpolar Current. Rev. Geophys.,24, 469–491.

  • Pacanowski, R. C., and S. G. H. Philander, 1981: Parameterization of vertical mixing in numerical models of tropical oceans. J. Phys. Oceanogr.,11, 1443–1451.

  • Park, Y. H., L. Gamberoni, and E. Charriand, 1993: Frontal structure, water masses and circulation in the Crozet Basin. J. Geophys. Res.,98, 12 361–12 385.

  • Quartly, G. D., and M. A. Srokosz, 1993: Seasonal variations in the region of the Agulhas Retroflection: Studies with GEOSAT and FRAM. J. Phys. Oceanogr.,23, 2107–2124.

  • Sarukhanian, E. I., and N. P. Smirnoff, 1986: Water Masses and Circulation of the Southern Ocean. Hydrometeorologisher Publ., Leningrad, 288 pp.

  • Semtner, A. J., and R. M. Chervin, 1988: A simulation of the Global Ocean circulation with resolved eddies. J. Geophys. Res.,93, 15 502–15 522.

  • ——, and ——, 1992: Ocean general circulation from a global eddy-resolving model. J. Geophys. Res.,97, 5493–5550.

  • Smith, R. D., J. K. Dukowicz, and R. C. Malone, 1992: Parallel ocean general circulation modeling. Physica D,60, 38–61.

  • Stevens, D. P., 1990: On open boundary conditions for three-dimensional primitive equation ocean circulation models. Geophys. Astrophys. Fluid Dyn.,51 (1–4), 103–133.

  • ——, and P. D. Killworth, 1992: The distribution of kinetic energy in the Southern Ocean: A comparison between observations and an eddy resolving general circulation model. Philos. Trans. Roy. Soc. London,338B, 251–257.

  • ——, and V. O. Ivchenko, 1997: The zonal momentum balance in an eddy-resolving general-circulation model of the Southern Ocean. Quart. J. Roy. Meteor. Soc.,123, 929–951.

  • Toggweiler, J. R., and B. Samuels, 1995: Effect of Drake Passage on the global thermohaline circulation. Deep-Sea Res.,42, 477–500.

  • Treguier, A. M., 1992: Kinetic energy analysis of an eddy resolving, primitive equation model of the North Atlantic. J. Geophys. Res.,97, 687–701.

  • ——, and J. C. McWilliams, 1990: Topographic influences on wind-driven, stratified flow in a β-plane channel: An idealized model for the Antarctic Circumpolar Current. J. Phys. Oceanogr.,20, 321–343.

  • Webb, D. J., P. D. Killworth, A. C. Coward, and S. R. Thompson, 1991: The FRAM Atlas of the Southern Ocean. Natural Environment Research Council, 67 pp.

  • Wilkin, J. L., and R. A. Morrow, 1994: Eddy kinetic energy and momentum flux in the Southern Ocean: Comparison of a global eddy-resolving model with altimeter, drifter, and current-meter data. J. Geophys. Res.,99, 7903–7916.

  • Wolff, J.-O., E. Maier-Reimer, and D. J. Olbers, 1991: Wind-driven flow over topography in a zonal β-plane channel: A quasigeostrophic model of the Antarctic Circumpolar Current. J. Phys. Oceanogr.,21, 236–264.

  • Fig. 1.

    (a) FRAM’s eddy kinetic energy in the top model layer (10.3 m), calculated over the last 6 years of the run. Contours are cm2 s−2 (after Ivchenko et al. 1997). (b) POP’s eddy kinetic energy in the top model layer (12.5 m). Contours are cm2 s−2. (c) Variance of the geostrophic velocity from TOPEX data (courtesy of P. Y. Le Traon). Contours are cm2 s−2 (after Ivchenko et al. 1997).

  • Fig. 2.

    The ACC regions: boxes A–C show the flow around Crozet Plateau, south of Australia (Macquarie–Ridge Complex), and Drake Passage, respectively. The contours show FRAM’s 6-yr time-mean streamfunction (top to bottom 10, 60, 130, and 180 Sv) to indicate the path of the ACC.

  • Fig. 3.

    FRAM time-mean streamfunction for the Crozet Plateau region. Contours in Sv.

  • Fig. 4.

    The EKE of the surface level for the Crozet Plateau region. Units are in cm2 s−2. (a) FRAM energy (depth 10.3 m). (b) POP energy (depth 12.5 m). (c) TOPEX velocity variances (courtesy P. Y. Le Traon).

  • Fig. 5.

    FRAM time-mean streamfunction for Macquarie–Ridge complex. Contours in Sverdrups.

  • Fig. 6.

    The EKE of the surface level for the Macquarie–Ridge complex. Units are in cm2 s−2. (a) FRAM energy (depth 10.3 m). (b) POP energy (depth 12.5 m). (c) TOPEX velocity variances (courtesy P. Y. Le Traon).

  • Fig. 7.

    FRAM time-mean streamfunction for Drake Passage region. Contours in Sverdrups.

  • Fig. 8.

    The EKE of the surface level for the Drake Passage region. Units are in cm2 s−2. (a) FRAM energy (depth 10.3 m). (b) POP energy (depth 12.5 m). (c) TOPEX velocity variances (courtesy P. Y. Le Traon).

  • Fig. 9.

    Partition of subregions. Streamlines indicate the time-mean flow. (a) The Crozet Plateau region, (b) Macquarie–Ridge complex, and (c) Drake Passage region.

  • Fig. 10.

    Time-mean and EKE balances for the Crozet Plateau northern and downstream regions. Units are cm2 s−2 for energy levels and 10−7 cm2 s−3 for energy transfer terms.

  • Fig. 11.

    (a) Time-mean and EKE split for the combined Macquarie–Ridge complex. Units are cm2 s−2 for energy levels and 10−7 cm2 s−3 for energy transfer terms. (b) Internal mode and external mode split for the EKE in the west subregion of Macquarie–Ridge complex. Units are cm2 s−2 for energy levels and 10−8 cm2 s−3 for energy transfer terms. (c) As for (b) except for east subregion of Macquarie–Ridge complex.

  • Fig. 12.

    Time-mean and EKE split for the upstream Drake Passage region. Units are cm2 s−2 for energy levels and 10−7 cm2 s−3 for energy transfer terms.

  • Fig. 13.

    Time-mean and EKE split for the northern branch of the Drake Passage region. Units are cm2 s−2 for energy levels and 10−7 cm2 s−3 for energy transfer terms.

  • Fig. 14.

    The averaged zonal velocity [u]zon in cm s−1. The velocity decreases monotonically with depth. The horizontal axis is latitude in °S. (a) For FRAM [u]zon at levels k = 1–17 (10.3–1945 m) (after Stevens and Ivchenko 1997) and (b) For POP [u]zon at levels k = 1–14 (12.5–1975 m).

  • Fig. 15.

    POP’s zonally averaged Reynolds stress at level 3 (depth 62.5 m). Lines 1, 2, 3, 4 represent the total stress ([]zon), standing eddy ([u*υ*]zon), overturning ([u]zon[υ]zon) and transient eddy ([uυ†]zon) components, respectively. The units of stress are cm2 s−2. The horizontal axis is latitude in °S.

  • Fig. 16.

    (a) Alongstreamline average of the along streamline component of velocity of the model ACC, for each of the upper 17 FRAM levels as a function of streamline, (cm s−1). The current decreases with depth from level 1 (10.3 m) to level 17 (1945 m). (b) Along constant sea surface height averaged tangential velocity, for each of the upper 14 POP model levels (cm s−1). The current decreases with depth from level 1 (12.5 m) to level 14 (1975 m). The horizontal axis corresponds to the negative surface height in cm.

  • Fig. 17.

    (a) Alongstreamline averaged Reynolds stress at level 2 in FRAM (32.5 m) and its components. Lines 1, 2, 3, 4 represent total, standing eddy, mean (overturning), and transient components, respectively. The units are Sverdrups and cm2 s−2 (after Ivchenko et al. 1996). (b) Along constant sea surface height averaged Reynolds stress at level 2 in POP (37.5 m) and its components. Lines 1, 2, 3, 4 represent total, standing eddy, mean (overturning), and transient components, respectively. The units are cm2 s−2. The horizontal axis corresponds to the negative surface height in cm.

  • Fig. 18.

    (a) Alongstreamline average of the total kinetic energy for the ACC in FRAM’s upper 17 levels, as a function of streamline. The energy decreases with depth from level 1 (10.15 m) to level 17 (1945 m). (b) The along constant sea surface height average of the total kinetic energy of POP’s ACC, for each of the upper 14 model levels, as a function of sea surface height. The units are cm2 s−2. The horizontal axis corresponds to the negative surface height in cm. The energy decreases with depth from level 1 (12.5 m) to level 14 (1975 m).

  • Fig. 19.

    Zonally averaged EKE in the second layer (37.5 m) for the POP. The solid line corresponds to POP5 and the the dashed line to POP7.

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